When possible, the person(s) who will be doing the work should be involved in the estimation and planning of the work. When you meet with a project team member to get an estimate, ask them when they can have it completed. Or ask them if it can be completed by (your deadline). If they say no, then you can move onward: discuss priorities with their boss, assign to another person, adjust the schedule, etc.
When you ask people to a meeting, request that they reply whether they can or can't attend. If they can't, then you should reschedule IF you really need that person. Most Calendar tools allow you to see free space on other peoples' calendars. If the person is not maintaining their calendar, that's another issue (probably discuss with them, then their boss if no improvement). If a person accepts a meeting and then doesn't show, they owe you an excuse or explanation; that's just proper courtesy.
It appears your problem is one or more of the following:
- your work has a lower priority that other tasks. You would need to discuss the relative priorities of the tasks with the person, and the person setting the priorities.
- there is some confusion regarding your role and/or authority. During a project, the Project Charter charges the Proj Mgr to complete the project and defines the authority given to the PM
I would discuss this situation with your boss, then evaluate what steps are necessary to correct the current situation.
The trouble with doing something right the first time is that nobody appreciates how difficult it was - Steven Wright